Estimation of non-constant variance in isothermal titration calorimetry using an ITC measurement model

Isothermal titration calorimetry (ITC) is the gold standard for accurate measurement of thermodynamic parameters in solution reactions. In the data processing of ITC, the non-constant variance of the heat requires special consideration. The variance function approach has been successfully applied in previous studies, but is found to fail under certain conditions in this work. Here, an explicit ITC measurement model consisting of main thermal effects and error components has been proposed to quantitatively evaluate and predict the non-constant variance of the heat data under various conditions. Monte Carlo simulation shows that the ITC measurement model provides higher accuracy and flexibility than variance function in high c-value reactions or with additional error components, for example, originated from the fluctuation of the concentrations or other properties of the solutions. The experimental design of basic error evaluation is optimized accordingly and verified by both Monte Carlo simulation and experiments. An easy-to-run Python source code is provided to illustrate the establishment of the ITC measurement model and the estimation of heat variances. The accurate and reliable non-constant variance of heat is helpful to the application of weighted least squares regression, the proper evaluation or selection of the reaction model.